L'l  E>  RAR.Y 

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OF    ILLINOIS 


AGRICULTURE 


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UNIVERSITY  OF  ILLINOIS 

Agricultural  Experiment  Station 


BULLETIN  No.  308 


THE  ENERGY  BASIS  OF  MEASURING 
MILK  YIELD  IN  DAIRY  COWS 

By  W.  L.  GAINES 


URBANA,  ILLINOIS,  MAY,  1928 


CONTENTS 

Page 
INTRODUCTION 403 

ESTIMATION  OF  ENERGY  VALUE 404 

From  the  Fat  and  Solids-Not-Fat 404 

From  the  Fat,  Protein,  and  Lactose 410 

By  Direct  Calorimetry 411 

Summary  of  Estimates • 413 

Discussion  of  Estimates : 413 

Interpretation  of  Formula 414 

FAT  PERCENTAGE  AND  FEED  REQUIREMENTS 415 

Data  from  Minnesota  Station 415 

Data  from  Copenhagen  Station 418 

FAT  PERCENTAGE  AND  YIELD  OF  MILK 419 

Correlation  Between  Fat  Percentage  and  Milk  Yield 419 

Shorthorn  Advanced  Registry 419 

Red  Danish  Advanced  Registry 423 

Red  Danish  Herd  Records 425 

Nature  of  the  Relationship 427 

SOME  ILLUSTRATIVE  APPLICATIONS 429 

Lactation  Curves 429 

Nutrition  Investigations 430 

Economic  Interpretation 431 

Genetic  Investigations 431 

SIGNIFICANCE  OF  FAT  PERCENTAGE 432 

SUMMARY  AND  CONCLUSIONS 434 

LITERATURE  CITED  .  .  .436 


THE  ENERGY  BASIS  OF  MEASURING 
MILK  YIELD  IN  DAIRY  COWSa 

W.  L.  GAIXES,  Chief  in  Milk  Production 

INTRODUCTION 

The  dairy  cow  is  maintained  primarily  as  a  milk  animal,  as  a  source 
of  human  food,  and  as  such  her  worth  depends  upon  her  milk  produc- 
tion. The  most  obvious  measure  of  the  milk  production  of  the  cow  is 
the  yield  of  milk  itself,  in  terms  of  weight  or  volume. 

It  has  come  to  be  a  somewhat  prevalent  practice  to  determine  and 
record,  by  some  systematic  method,  the  weight  of  milk  produced  by  in- 
dividual cows  in  dairy  herds.  Also,  since  the  advent  of  the  Babcock  test, 
it  is  usual  to  determine  the  percentage  fat  content  of  the  milk  by  some 
system  of  sample  taking  and  testing.  There  have  developed,  then,  two 
common  measures  of  the  performance  of  the  cow  at  the  pail:  (1)  the  milk 
yield  in  pounds  over  some  definite  period  of  time;  (2)  the  butterfat  yield 
in  pounds  over  the  same  period  of  time.  The  average  fat  percentage  is 
readily  derived  from  the  total  milk  and  fat  yields  and  is  likewise  com- 
monly reported. 

Milk  is  highly  variable  in  composition,  particularly  as  between 
different  cows  and  breeds.  It  always  contains  a  large  proportion  of 
water.  When  we  measure  production  of  the  cow  on  the  basis  of  milk 
alone,  we  place  the  water  of  the  milk  on  a  par  with  the  solids.  The  water 
of  milk  has  no  more  food  value  than  water  from  any  other  source,  and 
what  is  more  pertinent,  it  seems  that  the  production  of  the  water  frac- 
tion of  the  milk  requires  no  particular  expenditure  of  energy  on  the  part 
of  the  cow.  It  is  clear,  therefore,  that  milk  yield  alone  is  not  an  en- 
tirely satisfactory  measure  of  production. 

When  we  measure  production  on  the  basis  of  fat  alone,  we  ignore 
the  other  solids  of  the  milk.  These  other  solids  have  food  value,  and 
require  the  expenditure  of  energy  on  the  part  of  the  cow  in  their  pro- 
•  duction.  It  is  not  quite  proper  to  ignore  them. 

Another  measure  of  production  that  has  been  used  to  a  very  limited 
extent  is  based  on  the  total  solids  of  the  milk.  The  solids  of  milk  con- 
sist mainly  of  lactose,  fat,  protein,  and  ash.  Measuring  yield  on  the 
basis  of  total  solids  attaches  equal  importance  to  these  several  constit- 
uents according  to  their  amount. 


•Submitted  for  publication  December  29,  1927. 

403 


404  BULLETIN  No.  308  [May, 

In  Bulletin  245 19*  of  this  Station  it  was  proposed  that  the  gross  en- 
ergy value  of  the  milk  solids  be  used  as  a  measure  of  the  yield  of  dairy 
cows,  the  energy  value  to  be  estimated  in  terms  of  4-percent  milk  from 
the  milk  and  fat  yields.  Additional  evidence  on  the  subject  has  accum- 
ulated in  the  meantime,  which  seems  to  support  the  equity  of  the  energy 
measure.  Inasmuch  as  the  idea  seems  to  be  of  some  general  import  to 
those  concerned  with  the  milk  yields  of  dairy  cows,  it  is  purposed  in  this 
paper  to  submit  the  evidence  as  it  appears  at  the  present  time. 

ESTIMATION  OF  ENERGY  VALUE 

From  the  Fat  and  Solids-Not-Fat. — Stocking  and  Brew37*  have  pre- 
sented indirect  evidence  concerning  the  energy  value  of  milk,  based  on 
4,220  calories8  per  pound  of  fat  and  1,860  calories  per  pound  of  solids- 
not-fat.  Their  figures  lead  to  the  equation 

E  =  49.64M(2.66+/)  (1) 

where  E  is  energy  value  in  calories,  M  is  the  weight  of  milk  in 
pounds,  and  /  is  the  percentage  fat  content  of  the  milk. 

Equation  (1)  is  readily  transformed  to 

E'  =  AM  +  15F  (2) 

where  E'  is  energy  value  in  terms  of  pounds  of  average  milk  of  4-percent 
fat  content,  M  is  milk  in  pounds,  and  F  is  fat  in  pounds.b 

In  equation  (2)  E'  may  be  designated  "4-percent  milk,"  or  " fat- 
corrected  milk,"  or  "F.C.M.,"  and  we  may  write 

F.C.M.  =  AM  +  15F  (3) 

with  the  limitation  only  that  the  same  unit  of  weight  be  used  for  each  of 
the  three  terms. 

Equation  (3)  is  in  convenient  form  for  computation  from  the  pro- 
duction record  as  it  is  usually  kept  to  show  the  yield  of  milk  and  fat  by 
weight.  Where  the  average  fat  percentage  is  reported  it  may  be  con- 
venient to  employ  the  equivalent  equation 

"Thruout  this  paper  calorie  refers  to  the  large  calorie,  and  1,000  calories  =  1 
therm. 

bUtilizing  the  mathematical  relation,  M//100  =  F,  or  Mf  =  100F,  we  have 
total  energy  value  of  the  entire  quantity  of  milk 


E'  = 


energy  value  of  1  pound  of  4-percent  milk 
49.641T  (2.66 +/)      2.Q6M  +  M/       2.66M  +  100F 


49.64(2.66  +  4)  6.66  6.66 

=  .3994M  +  15.015F 

or,  in  round  numbers,  as  in  equation  (2),  and  this  gives  1  pound  of  4-percent  milk 
=  49.64  (2.66  +  4)  =  330.6  calories.  It  will  be  observed  that  the  coefficient 
(49.64)  of  M  in  equation  (1)  cancels  out  in  the  transformation  to  the  form  of 
equation  (2).  That  is  to  say,  equation  (2)  is  independent  of  the  absolute  value  of 
this  coefficient. 


1928]  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  405 

F.C.M.  =  M(A+  .15/)  (4) 

notation  as  before,  using  the  same  unit  of  weight  for  F.C.M.  and  M. 
Equation  (4)  is  in  useful  form  particularly  for  slide-rule  computation, 
where  one  scale  of  the  slide  rule  carries  graduations  of  ( .  4  +  .  15/)  for 
various  /  values  thru  the  range  required  (cf.  Fig.  1.  of  Gaines15*  and 
Fig.  3  of  Gaines16*). 

It  will  be  clear  that  equations  (1),  (2),  (3),  and  (4)  are  merely  differ- 
ent forms  to  express  the  same  thing.  The  question  arises,  with  what  de- 
gree of  accuracy  may  we  estimate  the  energy  value  of  the  milk  of  vari- 
ous individual  cows  from  the  weight  of  milk  and  its  fat  percentage  by 
the  use  of  these  equations? 

Five  sets  of  data  are  available  which  show  the  percentages  of  fat 
and  solids-not-fat  for  a  considerable  number  of  cows  over  part  or  all  of  a 
lactation  period.  The  Minnesota  Station24*  has  published  the  analyses  of 
543  samples  of  milk,  each  representing  the  milk  yield  for  one  week  of 
46  different  cows  in  the  Station  herd.  Various  breeds  and  stages  of  lac- 
tation are  represented.  The  solids  were  determined  gravimetrically,  the 
fat  in  part  gravimetrically  and  in  part  by  the  Babcock  method.  The 
Connecticut  Station39*  has  published  127  analyses,  each  representing  a 
complete  lactation  period,  for  50  cows  of  various  dairy  breeds  in  the 
Station  herd.  The  Wisconsin  Station41*  has  published  analyses  of  the 
milk  of  398  cows  of  various  dairy  breeds  in  the  Wisconsin  Cow  Competi- 
tion of  1909-1911.  For  the  most  part  the  period  covered  was  365  days 
within  the  same  lactation.  The  Holstein-Friesian  Association26*  has  pub- 
lished analyses  of  the  milk  of  458  registered  Holstein  cows  in  their  yearly 
advanced-registry  work.  The  American  Jersey  Cattle  Club1*  has  pub- 
lished analyses  of  the  milk  of  70  registered  Jersey  cows  for  120  days  at 
the  flush  of  lactation  in  the  contest  at  the  1904  St.  Louis  Exposition. 
Analyses  in  all  cases,  except  the  Minnesota  data,  were  by  the  Babcock 
and  lactometer  method. 

By  the  use  of  Stocking's  values  it  is  possible  to  calculate  the  calories 
per  pound  of  milk  from  the  above  analyses  and  then  to  determine  the 
correlation  between  the  fat  percentage  and  energy  value.  The  correla- 
tion surfaces  and  coefficients,  together  with  the  observed  regressions  and 
that  of  equation  (1),  give  an  index  of  the  accuracy  of  the  estimate  by 
the  equation.  The  correlation  surfaces  are  given  in  Table  1  and  the 
coefficients  in  Table  2.  The  mean  energy  values  derived  from  Table  1 
are  given  in  Table  3,  and  are  shown  graphically  in  Fig.  1,  together  with 
the  curve  of  equation  (1). 

It  is  clear  from  Fig.  1  that  the  equation  conforms  quite  closely  to 
the  observations.  The  equation  is  being  tested  here  against  data  not 
identical  with  those  from  which  it  was  derived.  The  good  agreement 


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ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows 


409 


TABLE  2. — COEFFICIENTS  OF  CORRELATION  BETWEEN  FAT  PERCENTAGE 
AND  ENERGY  VALUE  PER  POUND  OF  MILK  AND  BETWEEN  FAT 

PERCENTAGE  AND  SOLIDS-NOT-FAT  PERCENTAGE 

(Energy  value  estimated  on  the  basis  of  4,220  calories  per  pound  of  fat  and 
1,860  calories  per  pound  of  solids-not-fat) 


Source  of  data 

Fat  percentage 
and  energy  value 

Fat  percentage 
and  solids-not-fat 
percentage 

Minnesota  Station  

.9882+  .0007 

.801+  .007 

Connecticut  Station  

.9878+  .0015 

.684+  .032 

Wisconsin  Station  

.9915+  .0006 

.794+  .013 

Holstein-Friesian  Association  

.9152+  .0051 

.533+  .023 

American  Jersey  Cattle  Club  

.9668+  .0053 

.517+  .059 

shown  in  Fig.  1  and  the  high  coefficients  of  correlation  of  Table  2  may 
be  taken  to  mean  that  the  energy  value  of  milk  may  be  estimated  with 
considerable  accuracy  from  the  fat  percentage  and  weight  of  the  milk. 


TABLE  3. — MEAN  ENERGY  VALUES  PER  POUND  OF  MILK  AT  VARIOUS 

FAT  PERCENTAGES 

(Computed  on  the  basis  of  4,220  calories  per  pound  of  fat  and  1,860  calories 
per  pound  of  solids-not-fat) 


Fat 
percentage 

Computed 
by  equation 

CD" 

Source  of  data 

Minnesota 

Connecticut 

Wisconsin 

Holstein 

Jersey 

2.6 
2.8 
3.0 
3.2 
3.4 
3.6 
3.8 
4.0 
4.2 
4.4 
4.6 
4.8 
5.0 
5.2 
5.4 
5.6 
5.8 
6.0 
6.2 
6.4 
6.6 
6.8 
7.0 
7.2 

cals. 
261.1 
271.0 
281.0 
290.9 
300.8 
310.7 
320.7 
330.6 
340.5 
350.5 
360.4 
370.3 
380.2 
390.2 
400.1 
410.0 
420.0 
429.9 
439.8 
449.7 
459.7 
469.6 
479.5 
489.5 

cals. 

cals. 

cals. 
265.0 
280.0 
279.7 
291.5 
300.8 
312.5 
320.3 
331.4 
340.6 
349.7 
362.5 
370.3 
379.6 
389.2 
398.3 
408.5 
417.2 
427.0 
436.7 
445.0 

cals. 
255.0 
276.4 
280.4 
291.9 
302.0 
313.2 
322.5 
331.7 
341.0 
355.0 

cals. 

265.0 
275.4 
290.0 
296.0 
305.0 
315.0 
329.6 
342.3 
352.5 
361.6 
371.2 
382.2 
390.1 
399.6 
409.2 
419.1 
426.7 
439.2 
451.4 
458.0 
471.0 
480.0 
480.0 

270.0 
275.0 
292.8 
298.3 
313.0 
321.7 
330.7 
344.2 
350.3 
360.9 
365.0 
379.4 
383.8 
395.0 
407.5 
418.3 
430.0 
445.0 
448.3 

285.0 
297.5 
305.9 
317.3 
326.4 
340.0 
345.0 
355.0 
367.2 
370.0 
378.3 

"The  gross  energy  value  of  one  pound  of  milk  at  the  various  fat  percentages 
(as  will  appear  later)  actually  runs  about  3  percent  greater  than  the  values  given  in 
this  column. 


410 


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Percentage  fat  Conlenl  of  MilK(f) 

FIG.  1. — REL.\TION  BETWEEN  FAT  PERCENTAGE  AND  ENERGY  VALUE  ACCORDING  TO 

STOCKING'S  METHOD  OF  ESTIMATION 

The  energy  values  were  computed  on  the  basis  of  4,220  calories  per  pound 
of  fat  and  1,860  calories  per  pound  of  solids-not-fat.  The  smooth  curve  is  that  of 
equation  (1),  E  =  49.641f  (2.66  +  /),  derived  from  Stocking's  data.  It  will  be 
observed  that  the  equation  conforms  well  to  the  observed  energy  values  as  esti- 
mated but,  as  will  appear  later,  the  estimates  are  about  3  percent  lower  than 
the  actual  energy  values. 


It  is  of  course  apparent  that  assigning  a  fixed  energy  value  to  a 
pound  of  butterfat  necessitates  a  perfect  correlation  between  fat  per- 
centage and  energy  value  of  the  fat  per  pound  of  milk.  We  are  testing 
consequently  only  the  relation  between  fat  percentage  and  the  energy 
value  of  the  solids-not-fat  per  pound  of  milk.  The  correlation  between 
fat  percentage  and  solids-not-fat  percentage  gives  direct  evidence  of  this 
relation,  assuming,  as  we  are,  a  fixed  energy  value  per  pound  of  solids- 
not-fat.  The  coefficients  are  given  in  Table  2,  and  they  are  all  material- 
ly lower  than  the  fat  percentage  and  energy  value  coefficients. 

From  the  Fat,  Protein,  and  Lactose. — Andersen3*  has  approached  the 
estimation  of  the  energy  value  of  milk  in  a  more  accurate  manner  than 
that  of  Stocking.  Andersen  has  worked  from  the  analyses  of  the  milk 


1928}  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  411 

of  a  large  number  of  individual  cows  in  Denmark,  largely  of  the  Red 
Danish  and  Jersey  breeds.  From  his  data  he  derived  the  relations: 
p  =  1 . 597  +  .  446/  and  I  =  5 . 23  —  .  I/,  where  /,  p  and  I  are  respective- 
ly percent  of  fat,  protein,  and  lactose.  In  the  next  step  he  uses  the 
values  4,132,  2,658,  and  1,792  as  representing  the  calories  per  pound  of 
fat,  protein,  and  lactose  respectively.  Using  the  form  of  equation  (1), 
Andersen's  results  give  E  =  51.48M  (2.64  +/).  Using  the  form  of 
equation  (3),  we  have  F.C.M.  =  .398M  +  15.05F,  in  which  case  1 
pound  of  F.C.M.,  or  4-percent  milk,  =  341.8  calories. 

Hansson,25*  working  with  cows  in  Swedish  cow-testing  associations, 
found  that  there  is  a  close  relation  between  fat  percentage  and  energy 
value  per  unit  of  milk,  the  energy  value  being  estimated  in  a  manner 
similar  to  that  outlined  in  the  preceding  paragraph.  His  published  figures 
lead  in  the  form  of  equation  (1)  to  E  =  51.0731  (2.72  +/),  and  in  the 
form  of  equation  (3)  to  F.C.M.  =  .4048M  +  14.88F.  In  the  latter  case 
one  pound  of  F.C.M.,  or  4-percent  milkj  =  343.2  calories. 

By  Direct  Calorimetry. — Overman  and  Sanmann33'34*  have  investi- 
gated the  energy  value  of  milk  by  direct  and  precise  methods.  They 
have  reported  the  analyses  of  212  samples  of  milk  representing  in  part 
single  milkings  and  in  part  3-days'  milk  of  individual  purebred  and 
crossbred  cows  at  various  stages  of  lactation  in  the  University  of  Ill- 
inois dairy  herds.  The  analyses  included  a  gravimetric  determination  of 
the  fat  and  a  direct  calorimetric  determination  of  the  energy  value. 
The  correlation  between  the  fat  percentage  and  the  calories  per 
unit  weight  of  milk  was  found  to  be  r  =.9814  +  .0017,  Table  2.34* 
This  direct  evidence  shows,  therefore,  very  clearly  that  the  energy  value 
may  be  estimated  from  the  weight  of  milk  and  its  fat  percentage  with 
a  high  degree  of  accuracy.  Overman  and  Sanmann 's  results  in  the 
form  of  equation  (1)  give,  E  =  52.312M  (2.5064  +/),  and  in  the 
form  of  equation  (3),  F.C.M.  =  .38523f  +  15.37F.  In  the  latter 
case  1  pound  of  F.C.M.,  or  4-percent  milk,  =  340.3  calories. 

In  estimating  the  energy  yield  of  cows  we  are  often  concerned  with 
the  entire  lactation  or  a  considerable  portion  of  it,  rather  than  with  the 
short  periods  represented  by  single  samples.  Dr.  Overman  has  gener- 
ously allowed  the  writer  to  use  his  analytical  data  for  application  to  the 
appropriate  milk  yields  of  the  cows  in  order  to  secure  a  figure  applying 
to  a  longer  period  of  the  lactation.  Records  were  selected  of  all  those 
cows  having  three  or  more  3-day  composite  samples.  This  selection 
provided  76  samples  representing  sections  of  three  to  six  months  of  single 
lactations  of  21  different  cows.  Some  of  the  cows  were  purebred  and 
some  crossbred  dairy  stock. 


412 


BULLETIN  No.  308 


[May, 


When  treated  individually,  the  76  samples  show  a  correlation  be- 
tween fat  percentage  and  energy  value  per  unit  of  milk  of  r  =  .9761, 
with  the  regression  equation  E  =  51.38M  (2.69  +/).  When  the 
samples  are  treated  as  composites  so  as  to  deal  with  the  21  cows  as 
individuals,  the  correlation  works  out  at  r  =  .9860,  with  the  regres- 
sion equation  E  =  51.34M  (2.70  +/).  The  figures  for  the  21  cows 
as  individuals  give,  in  the  form  of  equation  (3),  F.C.M.  =  .403  M  + 
14.925F,  and  1  pound  of  F.C.M. ,  or  4-percent  milk,  =  344.0  calories. 

The  observed  fat  percentages  and  energy  values  for  the  21  cows 
are  shown  graphically  in  Fig.  2.  The  smooth  curve  is  that  of  equation 
(3)  adjusted  to  give  344.0  calories  at  4  percent  fat.  It  has  a  slope  of 


§380 

D_ 

k 

S"3SO 


Percentage  Fat  Content  of  Milk  (f) 

FIG.  2. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  ENERGY  VALUE 

DETERMINED  CALOKIMETRICALLY 

Each  circle  represents  a  section  of  3  to  6  months  of  a  single  lactation  of  an 
individual  cow.  The  smooth  curve  is  that  of  equation  (3)  in  which  1  pound 
F.C.M.  =  344.0  calories,  E  =  344  (AM  +  .15M/)  =  51. 6M  (2.66  +  /).  The  regres- 
sion equation  derived  from  the  coefficient  of  correlation  and  standard  deviations 
is  E  =  51.34M  (2.70  +  /).  The  curve  of  this  equation  is  indistinguishable  from 
the  one  given,  in  the  scale  of  the  figure. 


51.60  as  compared  with  the  slope  of  51.34  derived  above  from  the 
coefficient  of  correlation  and  standard  deviations,  or  least-squares  fit. 
The  difference  in  slope  of  the  two  curves  is  too  small  to  be  shown  in  the 
scale  of  Fig.  2.  The  correlation,  r  =  .9860,  and  the  graphic  presenta- 
tion of  Fig.  2  show  that,  so  far  as  these  analyses  indicate,  the  energy 
value  of  the  milk  of  the  cows  concerned  is  very  accurately  determined 
in  terms  of  4-percent  milk  by  equation  (3).  One  or  two  cows  show  a 
deviation  of  about  3  percent  from  the  formula,  but  most  of  them  lie 
very  close  to  it. 


1928}  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  413 

Summary  of  Estimates. — Equation  (3)  was  first  proposed  on  the 
basis  of  Stocking's  figures.  These  with  the  additional  data  mentioned 
above  may  be  summarized : 

Calories  per 

Authority  In  form  of  equation  (3)  pound  F.C.M. 

Andersen  F.C.M.  =  .3980M  +  15.  Q50F  341.8 

Hansson  F.C.M.  =  .4048M  +  14. 880F  343.1 

Overman"  F.C.M.  =  .3852M  +  15. 370F  340.3 

Overmanb  F.C.M.  =  .4030M  +  14.  Q25F  344.0 

Stocking  F.C.M.  =  .3994M  +  15.  Q15F  330.6 

Discussion  of  Estimates. — Clearly,  the  formula  AM  +  15F 
originally  derived  from  Stocking's  figures  is  justified  by  the  later 
evidence,  altho  the  absolute  value  in  calories  is  lower  than  that 
indicated  by  the  other  evidence.  Stocking  may  have  intended  his 
figures  to  represent  metabolizable  energy.  We  may  say  that  the 
gross  energy  value  of  1  pound  of  F.C.M.,  or  4-percent  milk  is  about\ 
340  calories. 

Overman  and  Sanmann33  •  34*  have  shown  that  the  energy  value 
of  milk  may  be  estimated  with  greater  accuracy  if  the  percentages 
of  protein  and  lactose  are  known  in  addition  to  the  percentage  of 
fat.  They  found  for  their  212  samples  a  multiple  correlation,  based 
on  fat,  protein,  and  lactose,  of  R  =  .9917;  as  compared  with  r  =  .9814, 
where  only  the  fat  percentage  was  used.c  The  protein  and  lactose  as 
well  as  the  fat  were  determined  by  accurate  chemical  methods. 

It  is  a  question  whether  an  estimate  of  the  solids-not-fat  by  the  use 
of  the  lactometer  would  permit  any  closer  estimate  of  energy  value  than 
may  be  made  from  the  fat  percentage  alone.  Overman  et  a£32*  have 
shown  that  even  where  the  specific  gravity  of  the  milk  is  determined 
with  greater  precision  than  is  possible  by  the  ordinary  application  of  the 
lactometer,  the  results  in  terms  of  solids-not-fat  are  apt  to  be  wide  of 
the  facts  as  determined  gravimetrically. 

One  may  note  also  in  Table  2  that  the  correlation  between  fat  per- 
centage and  solids-not-fat  percentage  is  much  lower  where  the  solids- 

8From  212  samples  of  the  milk  of  purebred  and  crossbred  dairy  cows. 

bFrom  three-months  to  six-months  sections  of  single  lactations  of  21  individual 
cows,  purebred  and  crossbred  dairy  stock. 

cThe  difference  of  .01  in  the  two  coefficients,  while  small  numerically,  has  a 
pronounced  meaning  in  terms  of  the  probable  errors  of  the  estimates  by  the  regres- 
sion equations.  In  theory  a  coefficient  of  rxy  =  .98  means  that  the  standard  devia- 
tion of  y  at  any  fixed  value  of  x  is  20  percent  of  the  standard  deviation  of  y  thru  the 
whole  range  of  x,  (VI  —  .982  =  .20).  Where  rtv  =  .99  the  corresponding  figure 
is  14  percent,  ( V 1  —  .992  =  .14).  The  probable  error  of  the  y  estimate  when  rn 
=  .98  is  therefore  reduced  by  30  percent  for  rz  =  .99,  [( .20  -  .14)/  .20  =  .30]. 


414  BULLETIN  No.  308  [May, 

not-fat  were  determined  by  lactometer  than  where  determined  gravi- 
metrically.  The  lower  coefficients  are  presumably  a  consequence  of  the 
inaccuracies  of  the  lactometer  method. 

Everything  considered,  it  appears  that  the  energy  yield  of  cows  may 
be  estimated  with  sufficient  accuracy  from  the  weight  of  milk  and  fat 
produced.  If  greater  precision  is  desired,  it  is  necessary  to  use  direct 
calorimetric  methods.  The  use  of  the  lactometer  as  an  aid  in  the  accu- 
racy of  the  energy  estimate  seems  to  be  entirely  unwarranted.  Even 
accurate  chemical  determination  of  the  protein  and  lactose  contribute 
comparatively  little  over  and  above  the  accuracy  attainable  by  the  use 
of  the  fat  determination  alone.  It  will  be  understood,  of  course,  that 
we  are  dealing  with  the  unaltered  normal  milk  of  the  cow. 

If  the  energy  yield  is  to  be  estimated  in  terms  of  4-percent  milk 
the  AM  +  15F  formula  answers  very  well.  This  basis  of  estimation 
is  independent  of  the  absolute  energy  value  of  the  milk,  and  it  was 
partly  for  this  reason  that  it  was  first  used,  since,  at  the  time,  the  ab- 
solute energy  value  did  not  appear  to  be  any  too  well  established.  The 
straightforward  scientific  procedure  would  be  to  determine  energy  yield 
calorimetrically,  and  while  the  calorimetric  determination  is  readily 
carried  out  in  the  chemical  laboratory,  it  is  not  adapted  to  use  in 
the  ordinary  and  extensive  keeping  of  production  records  of  cows  on 
the  farm;  hence  the  original  procedure  seems  still  to  be  justified.  If 
it  is  desired  to  express  the  energy  yield  in  terms  of  the  customary 
unit  of  the  calorie,  we  may  say  that  1  pound  of  4-percent  milk  equals 
340  calories,  and,  in  accord  with  the  AM  -f  15F  formula, 
E  =  51M  (2%  +/),  notation  as  before.  The  4-percent  milk  formula 
has  the  advantage  of  ease  of  computation  and  of  dealing  with  a  fa- 
miliar unit.  The  F.C.M.  yield,  however,  is  subject  to  confusion 
with  the  actual  milk  yield,  which  possibility  of  confusion  is  avoided 
by  the  calorie  formula.  There  would  be  some  justification  in  reserv- 
ing the  expression  of  yield  in  calories  for  such  precise  experimental 
work  as  actually  determines  the  energy  value  calorimetrically,  and  using 
the  "F.C.M.,"  or  "4-percent  milk,"  designation  for  the  indirect  esti- 
mate by  the  fat-percentage  formula. 

Interpretation  of  Formula. — The  use  of  equation  (3),  F.C.M.  =  AM 
+  15F,  is  not  to  be  regarded  as  a  process  of  assigning  weight  or  impor- 
tance to  the  milk  and  fat  respectively.  It  is  merely  an  algebraic  device 
adapted  to  the  computation  of  the  energy  yield,  in  terms  of  4-percent 
milk,  from  the  record  of  milk  and  fat  yield  as  ordinarily  reported. 

The  source  of  the  energy  value  of  milk  of  different  fat  percentages 
is  shown  diagrammatically  in  Fig.  3.  This  presents  Andersen's3*  scheme 
of  estimation,  namely:  EF  =  41 .32/,  EP  =  42.45  +  11 .85/  and  EL  = 


1928} 


ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows 


415 


93 . 72  —  1 . 79/,  where  EF  is  the  calories  in  1  pound  of  milk  due  to  the 
fat;  EP,  due  to  the  protein;  and  EL,  due  to  the  lactose.  In  a  rough  way 
one  might  say  that  AM  gives  a  constant  of  136  (=  A  X  340)  cal- 
ories per  pound  of  milk  due  to  a  nearly  constant  lactose  together  with 
a  nearly  constant  portion  of  the  protein;  while  15F  gives  the  variable 


500 


triergy  due  to  Protein  (Lpj  jy/// 


123456 

Percentage  Fat  Content  of  Milk,  (f ) 

FIG.  3. — SOURCE  OF  THE  ENERGY  VALUE  OF  MILK  ACCORDING  TO 

ANDERSEN'S  FORMULAS 

The  fraction  of  the  total  energy  value  of  the  milk  represented  by  the  fat, 
according  to  the  formulas  above,  is  41. 32//(  136.17  +  51. 38/).  The  fractions 
at  various  fat  percentages  are: 

/ 2  3  4  4.36  567 

Fraction 346  .427  .484  .500  .526  .558  .583 

That  is,  in  2-percent  milk  34.6  percent  of  the  energy  value  of  the  milk  is  in  the 
fat;  in  4.36-percent  milk  one-half  of  the  energy  value  is  in  the  fat;  while  in 
7-percent  milk  58.3  percent  of  the  energy  value  is  in  the  fat. 


calories  per  pound  of  milk  due  to  the  variable  fat  and  the  remaining, 
variable,  portion  of  the  protein  associated  with  the  variable  fat.a 


FAT  PERCENTAGE  AND  FEED  REQUIREMENTS 

Data  from  Minnesota  Station. — Milk  production  feeding  standards, 
expressing  the  result  of  much  experimental  and  practical  observation, 
are  adjusted  to  the  weight  of  the  cow  for  maintenance  requirements 
and  to  the  amount  and  fat  percentage  of  the  milk  for  lactation  require- 
ments. We  may  consider  the  system  based  on  digestible  nutrients  as 
formulated  by  Haecker.24*  From  Haecker's  published  results  it  is  pos- 
sible to  determine  the  correlation  between  the  percentage  fat  content  of 
the  milk  and  the  pounds  of  nutrients  for  lactation  (maintenance  re- 

•The  secretion  of  fat  and  the  secretion  of  protein  are  in  some  manner  quite 
intimately  related  in  the  general  physiology  of  milk  secretion  (cf.  Gaines,14*  Fig.  3). 


416 


BULLETIN  No.  308 


[Afay, 


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1928} 


ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows 


417 


quirements  excluded)  per  pound  of  milk  yielded.    The  correlation  sur- 
face is  given  in  Table  4,  and  leads  to  the  following  constants: 


Mean 

Standard  deviation 

Coefficient  of  correlation* 


Fat 

-percentage 
4.399 
.852 


Nutrients  for 
lactation  per  pound 

of  milk 
.3463  pounds 
.0636  pounds 


.648  ±  .033 


The  mean  observed  values  of  nutrients  for  lactation  per  pound  of 
milk  at  the  various  fat-percentage  classes  are  given  in  Fig.  4.  The  re- 
gression equation,  y  =  .1334+  .0484/,  derived  from  the  above  con- 
stants, shows  that  the  production  of  1  pound  of  4-percent  milk  requires 


§.34 


\ 


Percentage  rat  Content  of  Milk.  (1 ) 

FIG.  4. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  NUTRIENTS  FOR  LACTATION  PER 

POUND  OF  MILK  DERIVED  FROM  HAECKER'S  DATA 

The  equation  of  the  smooth  curve  is  that  of  equation  (3),  in  which  1  pound 
F.C.M.  requires  327  pounds  of  nutrients  for  lactation,  y  =  327 (AM  +  .l5Mf) 
=  .049(2.66  +  /).  The  regression  equation  derived  from  the  coefficient  of  corre- 
lation and  standard  deviations  is  y  =  .0484(2.76  +  /)  and  gives  a  curve  of  slightly 
less  slope  than  that  of  equation  (3),  but  the  difference  is  too  small  to  be  shown 
in  the  scale  of  the  figure. 


"This  coefficient  has  been  computed  by  the  use  of  four  different  groupings.  As 
a  matter  of  interest  in  statistical  method  the  results  are  given  below,  in  which  /  rep- 
resents fat  percentage  and  y  represents  pounds  of  nutrients  for  lactation  per  pound 
of  milk: 

Class  interval,  / 01 

Class  interval,  y 001 

Number  of  classes,  / 349 

Number  of  classes,  y 317 

Standard  deviation,  / 8571 

Standard  deviation,  y 06380 

SD,  X  SD, 05469 

Coefficient  of  correlation 6386 

It  works  out  in  this  particular  case  that  the  coarser  the  grouping,  the  higher 
the  coefficient  of  correlation.  In  the  finest  grouping  the  number  of  classes  actually 
represented  does  not,  of  course,  exceed  the  total  number  of  observations,  140. 


.1 
.01 

36 

34 

.8596 

.06404 

.05505 

.6411 


.2 

.02 

18 

16 

.8520 

.06363 

.05422 

.6479 


.5 

.03 

8 

11 

.8806 

.06479 

.05705 

.6596 


418 


BULLETIN  No.  308 


[May, 


.  327  pounds  of  digestible  nutrients  for  lactation  (maintenance  excluded). 
If  we  adjust  equation  (3)  to  this  value,  we  have  the  smooth  curve  of 
Fig.  4.  It  is  clear  at  once  that,  while  the  observed  values  of  Fig.  4  are 
somewhat  irregular,  their  trend  is  in  the  direction  of  the  energy  curve. 
The  energy  curve  crosses  the  least-squares  curve  at  /  =  4,  but  its  slope, 
.0491,  is  so  nearly  the  same  as  that  of  the  least-squares  curve,  .0484, 
as  to  make  the  two  practically  coincident  in  the  scale  of  Fig.  4. 

The  feed  energy  required  for  lactation  is  directly  proportional  to  the 
energy  value  of  the  milk  solids,  a  relationship  which  should  be  known  as 
HAECKER  's  LAW.  Therefore,  when  we  measure  production  in  terms  of 
F.C.M.  by  equation  (3),  we  measure  it  also  in  terms  of  the  nutrients 
required  for  lactation.  By  indirect,  but  altogether  straightforward, 
methods  it  has  been  shown13*  that,  within  the  same  breed,  and  so  far 
as  affected  by  the  percentage  fat  content  of  the  milk,  the  maintenance 
requirements  per  pound  of  milk  are  also  proportional  to  the  energy 
value  of  the  milk  solids  per  pound  of  milk. 

Data  from  Copenhagen  Station. — Frederiksen11*  has  presented  data 
which  indicate  that  the  total  feed  consumption  of  dairy  cows  is  propor- 
tional to  the  yield  of  F.C.M. ,  or  4-percent  milk.  His  figures  are  of  so 
much  interest  that  they  are  given  in  Table  5,  adapted  to  the  present 


TABLE  5. — PERCENTAGE  FAT  CONTENT  OF  MILK  AND  FEED  CONSUMPTION  PER 

POUND  OF  MILK 

Summary  of  ten  years'  (1909-1919)  results  of  the  Danish  crossbreeding  experi- 
ment, adapted  from  Frederiksen.  The  pertinent  point  of  interest  is  the  feed  con- 
sumption per  pound  of  F.C.M.  This  is  remarkably  constant,  as  measured  in  feed 
units.  The  Danish  feed  unit  is  1  kilogram  (2.2  pounds)  of  barley  or  its  equivalent. 


Breed  of  cows  

Red 

Crossbred 

Jersey 

Danish 

Number  of  cows  

368 

350 

353 

Age  of  cows,  in  years  

5.6 

5.8 

5.7 

Live  weight  per  cow,  in  pounds  

1021 

913 

796 

Percentage  fat  content  of  milk  

3.60 

4.28 

5.34 

Milk  per  cow  per  year,  in  pounds  

7934 

6389 

5018 

Fat  per  cow  per  year,  in  pounds  

286 

273 

268 

F.C.M.  per  cow  per  year,  in  pounds  

7458 

6657 

6027 

F.C.M.  per  pound  live  weight,  in  pounds.  .  .    . 

7  30 

7  29 

7.57 

Feed  units  per  cow  per  year   .    . 

3079 

2748 

2484 

Feed  units  per  pound  milk     

.388 

.430 

.495 

Feed  units  per  pound  F.C.M  

.413 

.413 

.412 

purpose.  This  table  gives  a  summary  of  ten  years'  (1909-1919)  results 
of  an  extensive  breeding  experiment  conducted  by  the  Counts  Ahlefeldt- 
Laurvig  in  cooperation  with  the  Copenhagen  Experiment  Station.  Two 
pure  breeds,  the  Red  Danish  and  the  Jersey,  were  used  at  the  start  in 
this  experiment.  These  two  breeds  were  intermated,  creating  a  third 


1928}  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  419 

breed  class  designated  as  crossbreds.  The  primary  purpose  of  the  in- 
vestigation was  to  determine  the  amount  and  economy  of  production  of 
the  three  breed  classes. 

Table  5  shows  that  the  three  breed  classes  differ  markedly  in  weight, 
in  milk  yield,  in  the  percentage  of  fat  in  the  milk,  in  amount  of  feed  con- 
sumed, and  in  amount  of  feed  per  unit  of  milk.  The  last  line  of  the  table 
shows,  however,  that  the  feed  consumption  per  pound  of  F.C.M.  is  the 
same  for  each  of  the  three  breed  classes.  Therefore,  when  we  measure 
production  in  terms  of  F.C.M.,  we  also  measure  it  in  terms  of  total  feed 
consumption,  so  far  as  the  average  results  of  these  three  groups  of  cows 
indicate.0 

FAT  PERCENTAGE  AND  YIELD  OF  MILK 

Correlation  Between  Fat  Percentage  and  Milk  Yield. — Dairy  liter- 
ature contains  some  confusion  of  thought  relative  to  the  relation  between 
the  richness  of  the  milk  and  the  amount  of  milk  yielded  by  individual 
cows.  In  general  it  is  recognized  that  these  two  variables  show  a  small 
negative  correlation.  Some  investigators  have  contended,  however,  that 
in  certain  breeds  the  correlation  is  zero.  There  are  many  factors  which 
have  a  very  great  effect  on  milk  yield,  and  this  makes  it  difficult  to  de- 
termine precisely  the  relation  between  fat  percentage  and  milk  yield, 
independently  of  all  other  variables. 

Gaines  and  Davidson,19* studying  the  regression  of  milk  yield  on  fat 
percentage  as  shown  by  a  large  number  of  yearly  and  7-day  records, 
reached  the  conclusion  that  milk  yield  is  affected  by  the  fat  percentage 
(composition)  of  the  milk,  and  that,  "so  far  as  affected  by  fat  percentage, 
the  milk  yield  is  inversely  proportional  to  the  energy  value  of  the  milk  solids 
per  unit  of  milk. "  That  is,  the  energy  yield  is  not  affected  by  the  fat 
percentage  of  the  milk.  Fig.  5  presents  the  method  of  attack  and  the 
results  for  one  set  of  Holstein  data.  Concordant  results  were  obtained 
also  for  the  Ayrshire,  Brown  Swiss,  Guernsey,  and  Jersey  breeds.  To 
the  evidence  from  the  records  of  these  breeds  may  now  be  added  similar 
evidence  from  the  Milking  Shorthorn  and  Red  Danish  breeds. 

Shorthorn  Advanced  Registry. — The  correlation  surface  for  fat  per- 
centage and  milk  yield  for  the  Milking  Shorthorns2*  is  given  in  Table 
6.  The  coefficient  of  correlation  works  out  at  r  =  —  .  227  ±  .  020.  Fig. 
6  shows  graphically  the  mean  milk  yields  at  the  various  fat  percentage 
classes,  and  the  constant  energy  curve.  The  energy  curve  conforms 

"It  is  of  interest  to  note  that  the  energy  yield  of  the  three  groups  of  cows  is 
nearly  proportional  to  their  weight.  Is  this  a  general  rule?  (cf .  footnote  on  page 
597  of  Gaines"*). 


420 


BULLETIN  No.  308 


[May, 


fl     215     U      29      3.1      3.3      3.5      3.7      3.9      41      43     45      47      49      5J       33     5.5 

Percentage  -Fat  content  or  MilK  (r) 

FIG.  5. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK 
YIELD:   HOLSTEIN  RECORDS 

This  figure  is  based  on  2,773  yearly  records  of  milk  yield  and  fat  percentage 
of  grade  and  purebred  Holstein  cows  in  Illinois  cow-testing  associations.  The 
method  of  studying  the  records  was  to  correlate  the  milk  yield  and  fat  percentage 
values,  which  gives,  r  =  — .229  ±  .012.  The  correlation  ratio  for  milk  yield  and  fat 
percentage  is,  TJ  =  242  ±  .012.  The  difference  between  the  two  is,  rf  —  r2  = 
.0061  ±  .0020,  statistical  evidence  that  the  regression  of  milk  yield  on  fat  per- 
centage deviates  significantly  from  a  straight  line. 

The  mean  milk  yields,  indicated  by  the  open  circles,  have  been  derived 
from  the  correlation  table.  Each  circle  represents  the  mean  milk  yield  of  a 
group  of  cows,  each  cow  of  the  group  lying  within  .05  of  the  fat  percentage  indi- 
cated by  the  base  line  scale.  It  appears  that  fat  percentage  is  not  correlated 
with  any  of  the  other  important  factors  affecting  milk  yield  (condition  of  the 
cow  at  calving  is  in  certain  cases  a  disturbing  exception  to  this  statement). 
Hence  we  may  assume  that  all  factors  other  than  fat  percentage  which  affect 
milk  yield  are  equal  or  counterbalanced  in  each  fat-percentage  group,  and  that 
the  differences  in  milk  yield  between  groups  are  due  to  differences  in  fat  per- 
centage. That  is,  inherent  lactation  capacity,  size,  age,  feed  supply,  days  in  milk, 
etc.,  are  assumed  to  average  the  same  in  each  group,  or  advantages  in  some  par- 
ticulars are  counterbalanced  by  disadvantages  in  the  other  particulars.  The  ideal 
of  this  assumption  will  be  realized  only  if  the  groups  are  large,  and  practically 
we  may  expect  considerable  irregularity  in  the  observed  yields,  which  in  fact 
occurs.  We  are  warranted  in  taking  a  smooth  curve  which  represents  the  trend 
of  the  observed  milk  yields  to  represent  the  true  relation  between  fat  percentage 
(composition  of  the  milk  as  measured  by  fat  percentage)  and  milk  yield. 

The  constant  energy  curve,  M  =  A/(2.Q6  +  /),  has  been  adjusted  to  the 
mean  milk  yields,  thus:  A  =  2n M0(2.66  +  /)/2n,  where  M0  is  the  observed 
milk  yield  and  n  is  the  frequency  at  each  fat  percentage  (/)  class.  This  gives 
A  =  43,668,  which  is  simply  the  average  energy  yield  shown  by  the  2,773  records, 
in  units  of  51  calories.  The  average  energy  yield  is  therefore  2,227  therms,  or 
6,550  pounds  F.C.M.  The  constant  energy  curve,  M  =  43,668/(2.66  +  /),  shows 
the  milk  yield  required  to  give  this  average  energy  value  at  the  various  fat  per- 
centages. It  describes  the  trend  of  the  observed  milk  yields  about  as  closely  as 
could  be  expected  of  any  simple  smooth  curve.  We  generalize,  then,  by  saying 
that  the  milk  yield  changes  with  the  fat  percentage  in  such  a  manner  that  the 
energy  yield  remains  constant,  that  is,  the  milk  yield  is  inversely  proportional 
to  the  calories  per  pound  of  milk. 

Perhaps  the  matter  may  be  presented  more  clearly  by  considering  the  en- 
ergy yields  directly,  instead  of  the  milk  yields.  The  energy  yields  are  repre- 
sented in  the  figure  in  terms  of  F.C.M.  by  the  solid  circles.  They  show,  of 
course,  the  same  sort  of  irregularity  as  the  milk  yields,  but  unlike  the  milk 
yields  they  show  no  consistent  variation  with  the  fat  percentage.  The  correlation 
between  the  F.C.M.  and  fat  percentage  values  is  r  =  — .010  ±  .013.  That  is  to 
say,  the  F.C.M.  yields  fluctuate  independently  of  the  fat  percentage. 


1928} 


ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows 


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422 


BULLETIN  No.  308 


[May, 


Percentage  Fat  Content  of  Milk,  (f ) 

FIG.  6. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK 

YIELD:   SHORTHORN  RECORDS 

This  figure  is  based  on  1,028  advanced-registry  yearly  records  of  Milking 
Shorthorn  cows.  The  plan  is  similar  to  that  of  Fig.  5.  Equation  of  the  curve  is 
Jf  =  56,293/(2.66 +  /).  The  average  energy  yield  is  2,871  therms  or  8,444 
pounds  F.C.M. 


fairly  well  to  the  trend  of  the  observations.  The  relation  between  fat 
percentage  and  milk  yield  in  these  Shorthorn  advanced-registry  records 
closely  resembles  that  found  previously19*  for  the  Guernsey  and  Jersey 
advanced-registry  records. 


Percentage  Fat  Content  of  Milk,  (f ) 

YIG.  7. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    RED 

DANISH  ADVANCED-REGISTRY  RECORDS 

This  figure  is  based  on  the  average  yearly  records  of  1,140  cows  in  the  Red 
Danish  advanced  registry.  The  plan  is  similar  to  that  of  Fig.  5.  Equation  of 
the  curve  is  M  =  67,926/(2.66  +  /).  The  average  energy  yield  is  3,464  therms 
or  10,189  pounds  F.C.M. 


ENERGY  BASIS  OF  MEASURING  MILK  YIELD  -IN  DAIRY  Cows  423 

Red  Danish  Advanced  Registry. — Similar  material  for  the  Red  Dan- 
ish breed  taken  from  the  herd  books36*  (Vols.  1-4,  1921-1924,  Cows  Nos. 
1000  to  2139)  is  presented  in  Table  7  and  Fig.  7.  The  records  of  Table  7 
represent  the  average  yearly  performance  of  the  cow  over  a  period  of 
3  to  14  years,  excluding  records  disturbed  by  abortion  or  records 
otherwise  misrepresentative.  As  a  rule,  calving  occurs  regularly  every 
year.  The  requirement  for  admission  to  the  herd  book  is  a  minimum 
average  yield  for  three  years,  or  more,  of  160  kilograms  of  "butter" 
(about  315  pounds  of  fat)  and  a  fat  test  of  not  less  than  3.6  percent; 
or,  175  kilograms  of  "butter"  (about  345  pounds  of  fat)  and  a  fat 
test  of  not  less  than  3.45  percent.  The  records  resemble  our  advanced- 
registry  records  in  that  a  certain  minimum  production  is  required 
for  admission  to  the  herd  book.  But  as  above  noted,  the  cows  repro- 
duce regularly  every  year,  and  in  this  respect  the  records  resemble 
our  cow-testing  association  records,  being  quite  different  from  the 
usual  advanced-registry  record. 

The  following  constants  are  derived  from  Table  7 : 


Mean  

Fat  percentage 
4.095 

M  ilk  yield 
10,068  pounds 

Standard  deviation  

.272 

1,171  pounds 

Coefficient  of  variability  .  . 

6.64 

11.63 

Coefficient  of  correlation —  .438  ±  .016 

It  will  be  noted  that  the  standard  deviation  or  variability  for  both 
variables  is  very  low,  a  result  presumably  of  the  entrance  restrictions 
and  the  use  of  average  records  for  the  individual  cows.  The  correla- 
tion between  fat  percentage  and  milk  yield,  r  =  — .  438,  is  closer  than 
any  found  heretofore  in  dealing  with  yearly  records.  This  high  corre- 
lation is  probably  a  result  of  dealing  here  with  three-year-or-more  aver- 
ages. 

The  mean  milk  yields  are  shown  graphically  in  Fig.  7,  together  with 
the  constant  energy  curve.  The  latter  is  based  on  the  average  energy 
yield  of  the  1,140  records,  3,464  therms  or  10,189  pounds  F.C.M.  This 
curve  plainly  describes  the  general  trend  of  the  observed  milk  yields 
quite  well  except  at  the  lower  fat  percentages.  It  has  been  shown  else- 
where (page  587  of  Gaines  and  Davidson19*)  that  the  fixed  fat-produc- 
tion requirement  of  the  advanced  registry  is  the  more  severe  the  lower  the 
fat  percentage,  and  hence  tends  to  raise  the  mean  milk  yields  at  the  lower 
fat  percentages.  In  the  present  case  we  have  also  a  marked  increase 
in  the  fat-yield  entrance  requirement  of  the  two  classes  at  /  =  3.5  and 
3 . 6,  which  of  course  makes  these  two  observations  unduly  high. 


424 


BULLETIN  No.  308 


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ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows 


425 


Red  Danish  Herd  Records. — Records  of  the  Red  Danish  breed  which 
correspond  closely  to  our  cow-testing  association  records  are  given  in 
Table  8  and  graphically  in  Fig.  8.  The  data  of  Table  8  are  derived  from 
the  published6*  records  of  the  Count  Ahlefeldt  herd  referred  to  above 
in  connection  with  the  relation  between  fat  percentage  and  feed  con- 
sumption per  pound  of  milk.  Yearly  records  of  less  than  250  days  of 
lactation  have  been  excluded  in  the  present  computations.  Otherwise, 
all  records  were  used  of  the  Red  Danish  breed  that  appear  in  the  first 
to  fourteenth  annual  reports  (1905-1919),  except  the  third  report  (1907- 
1908),  which  latter  was  not  available. 

The  constants  derived  from  Table  8  are  as  follows: 


Mean 

Standard  deviation ..-..., 
Coefficient  of  variability . 
Coefficient  of  correlation . 


Fat  percentage 

3.544 
•      .295 
8.31 
..-.185  + 


Milk  yield 
7,527  pounds 
1,679  pounds 
22.31 


.029 


A  comparison  of  Tables  7  and  8  and  of  the  derived  constants  gives 
some  indication  of  the  effect  of  the  selection  practiced  in  the  advanced- 
registry  records.  The  advanced-registry  data  show  a  higher  milk  yield 
and  fat  percentage  and  lower  variability.  A  large  number  of  the  lower- 
fat-percentage  cows  are  cut  out  in  the  advanced-registry  records. 


Percentage  Fat  Content  of  Milk,  (f ) 

FIG.  8. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    RED 

DANISH  HERD  RECORDS 

This  figure  is  based  on  511  yearly  records  of  Red  Danish  cows  in.  the  herd 
of  Count  Ahlefeldt.  The  plan  is  similar  to  that  of  Fig.  5.  Equation  of  the 
•curve  is  M  =  46,568/(2.66  +  /).  The  average  energy  yield  is  2,375  therms,  or 
6,985  pounds  F.C.M. 


The  correlation  between  fat  percentage  and  milk  yield  in  these  herd 
records,  r  =  —  .  185,  is  of  about  the  same  order  of  magnitude  as  usually 
found  for  yearly  data  of  these  variables  in  the  lower  testing  breeds.  Of 


426 


BULLETIN  No.  308 


[May, 


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1928}  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  427 

principal  interest  is  the  regression  of  milk  yield  on  fat  percentage  as 
shown  in  Fig.  8.  The  average  energy  yield  of  the  511  records  is  2,375 
therms,  or  6,985  pounds,  F.C.M.  The  constant  energy  curve  of  Fig. 
8  represents  this  value  thruout,  and,  except  for  some  deviations  at  either 
fat  percentage  extreme,  it  conforms  reasonably  well  with  the  observed 
milk  yields. 

Nature  of  the  Relationship. — Milk  secretion,  as  it  has  become  quan- 
titatively developed  in  the  dairy  cow,  requires  a  very  great  expenditure 
of  energy.  It  seems  reasonable  to  suppose  that  on  the  average  a  3-per- 
cent cow  should  do  as  much  work  as,  and  no  more  than,  a  4-percent  cow, 
or  a  5-percent  cow,  if  all  factors  such  as  size  and  age  are  equalized. 
It  seems  reasonable  further  that  the  work  performed  by  the  cow  in 
milk  secretion  should  be  proportional  to  the  product  of  that  work  as 
measured  in  terms  of  calorific  value.3  Haecker's  work  and  the  results 
of  the  Copenhagen  experiment  confirm  the  latter  proposition. 

The  nature  of  the  relationship  between  fat  percentage  and  milk 
yield  seems  to  indicate  that  the  energy  required  in  milk  secretion 
is  a  limiting  factor  in  the  amount  of  milk  secreted,  and  the  amount 
of  energy  devoted  to  milk  secretion  is  independent  of  the  particular 
proportions  in  which  the  several  milk  constituents  are  elaborated. 
On  the  basis  of  such  a  physiological  interpretation  we  should  expect 
to  find  no  exceptions  so  far  as  any  particular  breed  of  cows  is  con- 
cerned. 

In  this  connection  the  negative  correlation  between  fat  percentage 
and  milk  yield  found  above  for  the  Red  Danish  breed  is  of  special  in- 
terest because  of  the  fact  that  Ellinger9*  has  reported  a  correlation  of 
r  =  .055  ±  .044  for  this  breed  in  the  Count  Ahlefeldt  herd.  He  dealt, 
however,  with  only  the  first  ten  weeks  of  the  lactation  and  it  seems 

8In  some  cases  glandular  activity  is  partly  manifest  in  a  difference  in  the  osmot- 
ic pressure  of  the  secretion  and  the  osmotic  pressure  of  the  blood.  The  urine,  for 
example,  may  be  of  much  higher  osmotic  pressure  than  the  blood  and  in  such  case 
the  kidney  has  expended  energy  and  performed  work  in  this  particular  (cf.  Baylis,5* 
pages  339-343).  A  striking  characteristic  of  the  milk  of  the  cow  (and  probably  all 
mammals)  is  that  its  osmotic  pressure  is  the  same  as  that  of  the  blood  which  nour- 
ishes the  gland;  and  the  osmotic  pressure  of  the  blood  in  health  varies  only  within 
very  narrow  limits.  In  milk  secretion  there  is  no  balance  of  osmotic  energy  with 
which  to  reckon,  unless  it  requires  energy  on  the  part  of  the  cell  to  maintain,  for  in- 
stance, a  lower  concentration  of  sodium  chlorid  in  the  milk  than  exists  in  the  blood. 
If  the  quantity  of  water  in  the  milk  is  determined  by  osmotic  forces  (as  seems  likely) 
without  net  expenditure  of  energy,  then  it  seems  clear  enough  that  the  water  of  the 
milk  should  be  ignored  in  any  quantitative  measure  of  milk  yield  for  biological 
study  of  dairy  capacity.  To  do  otherwise  places  undue  emphasis  on  the  lactose  of  the 
milk  (cf.12.  "•  28-  29« 38*). 


428  BULLETIN  No.  308  [May, 

that  his  peculiar  result  is  in  some  way  connected  with  this  early  stage 
of  lactation,  since  as  shown  above,  the  usual  negative  correlation  ob- 
tains when  dealing  with  the  yearly  records  in  the  same  breed  and  herd.8 


•Some  other  investigators  have  reported  practically  zero  correlation,  or  even 
positive  correlation,  between  fat  percentage  and  milk  yield,  but  so  far  as  the  writer 
has  observed,  there  was  always  some  plausible  reason  to  believe  that  extraneous  fac- 
tors were  entering  in  to  disturb  the  true  relation.  For  example,  in  certain  Holstein 
records  special  feeding  and  management  practices  may  render  the  records  unsuitable 
to  reveal  the  true  relationship.  This  is  especially  the  case  in  the  later  7-day  records 
made  shortly  after  calving  (cf.  Fig.  4  of  Gaines18*). 

Langmack30*  has  published  an  extensive  series  of  correlations  between  fat  per- 
centage and  milk  yield  for  the  separate  lactation  periods  of  the  same  cow.  If  we  could 
have  the  same  cow  produce  alternately,  for  certain  periods,  milk  of  a  prescribed  fat 
percentage,  with  other  conditions  remaining  constant,  we  would  have  a  direct  way  of 
measuring  the  influence  of  fat  percentage  (composition  of  the  milk)  on  the  yield  of 
milk.  Unfortunately  this  is  a  condition  impossible  of  experimental  control,  and  hence 
we  must  depend  on  the  indirect  evidence  of  some  such  statistical  device  as  that  of 
Fig.  5.  In  Langmack's  procedure  there  is  some  fluctuation  in  fat  percentage  from  one 
lactation  to  another.  But  the  age  of  the  cow  is  certainly  changing,  and,  for  immature 
ages,  her  weight  (size)  also.  Age  and  weight  are  both  powerful  factors  affecting  pro- 
ductive capacity,  and  hence  it  is  not  permissible  to  attribute  changes  in  milk  yield 
from  lactation  to  lactation  as  due  entirely,  or  even  to  any  important  extent,  to  dif- 
ferences in  fat  percentage.  About  two-thirds  of  Langmack's  coefficients  were  nega- 
tive and  one-third  positive.  The  negative  correlation  is  in  accord  with  the  known 
pronounced  tendency  for  milk  yield  to  increase  with  age  (in  cows  under  8  or  9  years 
of  age,  which  constitute  the  great  majority  of  the  population),  and  the  slight  tend- 
ency for  the  fat  percentage  to  decrease  with  age.  The  positive  correlations  indicate, 
however,  that  a  considerable  proportion  of  the  individual  cows  have  a  slight  tend- 
ency for  the  fat  percentage  to  increase  with  age.  It  would  not  be  proper  to  interpret 
Langmack's  positive  correlations  as  conflicting  with  the  theory  that,  so  far  as  affected 
by  the  fat  percentage  (composition)  of  the  milk,  the  milk  yield  is  inversely  propor- 
tional to  the  energy  value  per  pound  of  milk.  Neither  do  his  negative  correlations 
lend  any  support  to  the  theory. 

Since  this  paper  was  prepared  there  has  come  to  hand  Missouri  Research  Bulle- 
tin 105,  by  Samuel  Brody,  entitled  "Growth  and  Development  with  Special  Reference 
to  Domestic  Animals:  X,  The  Relation  Between  the  Course  of  Growth  and  the  Course 
of  Senescence  with  Special  Reference  to  Age  Changes  in  Milk  Secretion."  On  the 
relation  between  fat  percentage  and  milk  yield  Brody  uses  the  equation  M  =  Cf~k 
in  which  M  and  /  are  in  the  present  notation  and  C  and  k  are  constants.  This  is  a 
very  interesting  form  of  expression  and  undoubted!}7  capable  of  describing  the  re- 
lation with  accuracy.  Just  what  biological  meaning  may  be  attached  to  the  constants 
is  not  clear. 


1928] 


ENEBGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows 


429 


SOME  ILLUSTRATIVE  APPLICATIONS 

Lactation  Curves. — An  illustration  of  the  application  of  energy 
values  to  the  lactation  curves  of  farrow  Guernsey  cows,  has  been  pre- 
sented heretofore  (Fig. I20*).  It  was  there  shown  that  the  energy  lacta- 
tion curve  is  more  regular  than  the  milk  or  fat  lactation  curves.  Sim- 
ilar material  is  presented  here  in  Fig.  9  taken  from  Ellinger's10*  data  on 
the  Red  Danish  breed. a  It  is  evident  from  the  graph  and  from  the 
numerical  values  given  in  the  legend,  that  the  energy  lactation  curve  is 
much  more  regular  than  the  milk  or  fat  lactation  curves. 


Time  after  Calving  -  Weeks  (t) 


FIG.  9. — LACTATION  CURVES  OF  RED  DANISH  Cows 

This  figure  shows  for  the  first  lactation  periods  of  Red  Danish  cows  the 
rate  of  milk  yield  (M'),  the  rate  of  F.C.M.  yield  (F.C.M/),  and  the  rate  of  fat 
yield  (F')  in  pounds  per  day  with  advance  in  lactation.  The  curves  are  of  the 
exponential  type,  rate  oj  yield  =  Ae  -*«.  They  have  been  fitted  by  the  method 
of  least  squares,  excluding  the  first  observation.  (For  details  of  method  of 
fitting  cf.  Games15'20*).  The  equations  are:  M'  =  28.25e  ~ -017"' ;  F.C.M.'  = 
25.55e  ~-01468« ;  and  F'  X  25  =  23.78e  " -01468'.  The  relative  root-mean  square  errors 
\veighted  by  I/A  are:  F.C.M.,  100;  F,  487,  and  M,  476.  The  F.C.M.  observa- 
tions thus  agree  much  more  closely  with  their  smooth  curve  than  do  the  fat  or 
milk  observations  with  theirs. 

The  constant  of  proportionality,  k,  shows  the  rate  of  decrease  per  week  in 
the  rate  of  yield.  The  rate  of  decrease  per  month  would  be  4.345fc.  The  rate 
of  decrease  in  energy  yield  is  therefore  6.38  percent  per  month.  This  figure  is 
for  young  cows;  for  older,  higher-yielding  cows  the  rate  of  decrease  would  un- 
doubtedly be  considerably  greater  (cf.  Fig.  28  of  Gaines16*). 


If  we  choose  to  regard  the  cow  as  a  machine,  the  energy  lactation 
curve  may  be  translated  directly  as  representing  the  horsepower  de- 
livered by  the  machine.  This  point  of  view  may  be  justified  by  the 
fact,  as  above  pointed  out,  that  the  feed  energy  required  for  lactation 
is  proportional  to  the  milk  energy.  On  the  basis  that  1  pound  of 

"The  writer  is  indebted  to  Dr.  Ellinger  for  the  numerical  data,  which  were  pre- 
sented only  graphically  in  the  reference  given. 


430  BULLETIN  No.  308  [May, 

F.C.M.  =  340  calories,  and  on  the  basis  of  the  mechanical  equivalent 
of  heat  that  1  calorie  =  3,084  foot-pounds,  we  have  1  pound  F.C.M. 
=  1,048,560  foot-pounds  and  1  pound  F.C.M.  per  day  =  .022  horse- 
power. Accordingly,  in  Fig.  9  we  would  have  a  maximum  power  out- 
put of  .533  (=  24.23  X  .022)  horsepower,  which  gradually  declines 
with  time,  finally  reaching  zero  with  the  cessation  of  lactation. 

This  interpretation  may  serve  to  indicate  the  broad  nature  of  the 
energy  measure.  It  clearly  puts  the  performance  of  the  cow  on  a  dy- 
namical basis. 

Nutrition  Investigations. — Hansson25*  says,  "Die  beste  Grundlage 
zur  Berechnung  des  Nahrungsbedarfs  der  Kiihe  bei  der  Produktion  von 
Milch  mit  verschiedenem  Fettgehalte  ist  der  Kalorienwert  der  Milch  je 
Kilogramm. "  (The  best  basis  of  reckoning  the  food  requirement  of  cows  for 
the  production  of  milk  of  different  fat  content  is  the  calorific  value  of  the 
milk  per  kilogram.)  The  advantage  of  measuring  milk  yield  on  an  en- 
ergy basis  for  nutritional  studies  seems  to  be  so  plain  as  to  require  no 
extended  discussion.  For  very  refined  investigations  it  would  be  de- 
sirable to  have  direct  determinations  of  the  energy  value  of  the  milk  by 
the  calorimeter.  For  the  usual  feeding  trials  equation  (3),  page  404  or 
the  equivalent  calorie  formula,  page  414  would  seem  to  be  amply  accu- 
rate.8 


"It  may  be  of  interest  to  take  any  of  the  dairy  feeding  standards  and  compute 
the  nutrients  required  at  various  fat  percentages  for  one  pound  F.C.M.  The  re- 
sults will  be  found  substantially  constant. 

Haecker's  data  as  above  analyzed  lead  to  the  formula,  Pounds  of  digestible 
nutrients  for  lactation  =  .327  F.C.M.  His  standard  for  maintenance  is,  Pounds 
digestible  nutrients  for  maintenance  per  year  =  2 . 893  W,  where  W  is  li ve  weight  of 
the  cow  in  pounds.  It  is  of  interest  to  compare  the  observed  feed  consumption  of 
Table  5  (1  feed  unit  =  1  kilogram  of  barley  =  1.75  pounds  of  digestible  nutrients) 
with  the  requirements  computed  by  Haecker's  formulas: 

Red  Danish     Crossbred     Jersey 

Pounds  digestible  nutrients  consumed,  observed 5,388  4,809          4,347 

Pounds  digestible  nutrients  required,  computed 5,393  4,818          4,274 

This  is  a  rather  remarkable  agreement  between  theory  and  observation. 

Since  this  paper  was  prepared  there  has  come  to  hand  Wisconsin  Research 
Bulletin  79,  by  M.  J.  B.  Ezekiel,  P.  E.  McNall,  and  F.  B.  Morrison,  entitled  "Prac- 
tices Responsible  for  Variations  in  Physical  Requirements  and  Economic  Costs  of 
Milk  Production  on  Wisconsin  Dairy  Farms."  Fig.  6  of  this  Wisconsin  bulletin 
presents  three  sets  of  data  from  farm  records  from  the  states  of  Wisconsin,  Virginia, 
and  Pennsylvania,  showing  the  relation  between  fat  percentage  and  the  yield  and  feed 
cost  of  the  milk.  The  three  sets  of  data  are  not  in  the  closest  agreement  among  them- 
selves, a  result  possibly  of  the  difficulty  of  accurately  evaluating  all  the  factors  in- 
volved, particularly  pasture.  The  results  from  the  Wisconsin  farms  agree  fairly  well 
with  the  proposition  that  feed  cost  in  nutrients  is  proportional  to  the  energy  value  of 
the  milk. 


192S\  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  431 

Economic  Interpretation. — Certain  economic  aspects  of  equation  (3) 
have  been  presented  in  detail  elsewhere13- 17*  and  it  is  sufficient  here  to 
say  that  the  cost  of  producing  milk,  so  far  as  affected  by  the  fat  per- 
centage of  the  milk,  is  proportional  to  the  energy  value  of  the  milk. 
There  is  a  growing  disposition  on  the  part  of  whole-milk  buyers  to  ad- 
just the  price  of  milk  according  to  its  fat  test,  and  there  seems  to  be  a 
tendency  for  this  adjustment  to  align  more  or  less  closely  with  the  en- 
ergy value  of  the  milk  (cf.  Fig.  2  of  Gaines13*). 

Genetic  Investigations. — A  possible  use  of  energy  yield  in  genetical 
analysis  may  be  illustrated  by  a  hypothetical  case.  Suppose  we  have 
two  pure  races  of  cattle,  one  of  which  has  a  genetic  capacity  of  an  annual 
yield  of  10,000  pounds  of  3.5-percent  milk,  and  the  other  7,551  pounds 
of  5.5-percent  milk.  If  these  two  races  are  hybridized,  we  might  an- 
ticipate obtaining  a  certain  proportion  of  F2  segregates  which  had  a 
capacity  of  10,000  pounds  of  5 . 5-percent  milk.  But  if  we  take  the  en- 
ergy yield  as  the  measure  of  production,  we  find  the  two  races  have  the 
same  capacity,  namely,  9,250  pounds  F.C.M.,  and  consequently  we 
should  expect  all  the  F2  generation  to  be  of  the  9,250-pound  class,  as- 
suming that  the  capacity  of  9,250  pounds  F.C.M.  of  the  two  original 
pure  races  was  determined  by  similar  factors. 

While  we  are  speculating,  let  us  consider  a  still  wider  divergence 
in  the  orginal  stock.  The  reindeer  produces  milk  containing  22  per- 
cent of  fat.4*  It  is  not  extraordinaiy  to  conceive  of  a  Holstein  cow  pro- 
ducing in  365  days  20,000  pounds  of  3.3-percent  milk.  Many  cows  have 
exceeded  that  performance.  Suppose  such  a  race  is  crossed  with  the  rein- 
deer (assuming  for  the  sake  of  the  argument  that  such  a  cross  would  be 
fertile)  should  we  obtain  in  the  F2  generation  an  occasional  female 
segregate  producing  20,000  pounds  of  22-percent  milk  in  365  days 
under  favorable  environmental  conditions?  Considered  from  the 
energy  viewpoint,  we  should  expect  nothing  of  the  kind,  for  the 
reindeer's  energy-yield  capacity  is  a  mere  fraction  of  that  of  the 
Holstein,  and  we  should  be  lucky,  therefore,  to  recover  in  F2  even 
the  original  capacity  of  the  Holstein  ancestor.* 

Various  breeding  operations  have  been  entered  into  at  various  times 
by  various  people  with  the  idea  of  obtaining  an  improved  dairy  cow  as 
a  high-milk  and  high-fat-percentage  segregate,  on  the  basis  that  milk 
yield  and  fat  percentage  are  not  correlated.  The  above  noted  crossing 
of  the  Red  Danish  and  Jersey  breeds  is  an  example,  and  much  wider 

•The  foregoing  speculation  assumes  inheritance  and  segregation  in  accordance 
with  Mendelian  principles.  The  actual  inheritance  of  milk  yield  and  composition 
of  the  milk  is  a  very  complicated  affair,  necessitating,  on  the  Mendelian  interpreta- 
tion, the  assumption  of  multiple  factors  (cf.  '•  "•  12-  «•  22-  "-  35-  43*). 


432  BULLETIN  No.  308  [May, 

crosses  have  been  made,  as  mating  a  zebu  male  with  Holstein  females. 
The  results  of  such  crossings  do  not  appear  to  promise  the  realization  of 
increased  capacity  by  such  methods.  To  a  certain  extent,  therefore, 
these  hybridizing  results  may  be  regarded  as  experimental  evidence  that 
the  energy  yield  is  a  more  fundamental  measure  of  performance  than  is 
the  milk  yield. 

An  experiment  to  demonstrate  the  possibility  of  improving  the 
dairy  production  of  the  daughters  of  scrub  cows  by  the  use  of  purebred 
dairy  bulls,  has  been  carried  out  at  the  Iowa  Experiment  Station.  In 
one  case  the  average  of  three  lactations  of  a  certain  scrub  cow  and  six 
lactations  of  a  certain  daughter  of  the  cow  by  a  Holstein  bull  are  given31* 

as: 

M  F  f  F.C.M. 

Dam 3,874 .6  192 .62  4 .97  4,439 

Daughter 6,955 .5  266 .25  3 .83  6,776 

Daughter/dam 1 .795  1 .382  .771  1 .526 

The  daughter's  production  shows  thus  an  increase  of  80  percent  in  milk 
and  38  percent  in  fat  over  and  above  that  of  the  dam.  The  actual  in- 
crease in  work  accomplished  (F.C.M.  yield)  by  the  daughter  is  53  per- 
cent. This  may  appeal  to  the  reason  as  being  a  better  expression  of  the 
improvement  effected  by  the  sire.a 

The  dairyman  who  is  selling  whole  milk  at  a  fixed  price  per  hun- 
dredweight may  argue  that  he  is  concerned  only  with  the  increase  in  milk 
yield.  Likewise,  the  one  who  is  selling  cream  may  argue  that  he  is  con- 
cerned only  with  the  increase  in  fat  yield.  But  if  the  biologically  im- 
portant measure  of  activity  of  the  mammary  gland  is  the  energy  value 
of  the  milk  solids,  as  seems  to  be  sufficiently  evident  from  the  citations 
of  the  foregoing  pages,  then  what  the  dairyman  needs  first  of  all  is  a  high- 
energy-yielding  (hard-working)  cow.b  If  economic  conditions  are  such 
that  milk  has  money  value  only  according  to  weight,  then  he  will  nat- 
urally want  that  high-energy-yielding  cow  which  gives  milk  with  a  mini- 
mum energy  value  per  pound,  that  is  the  cow  with  low  fat  percentage. 
If  economic  conditions  are  such  that  only  the  fat  of  the  milk  has  money 
value,  then  he  will  want  that  high-energy-yielding  cow  which  devotes 
the  largest  part  of  the  energy  of  lactation  to  the  production  of  fat.  This 
is  the  cow  with  high  fat  percentage,  as  is  clearly  shown  in  Fig.  3. 

SIGNIFICANCE  OF  FAT  PERCENTAGE 

The  percent  of  fat  in  milk  has  been  very  extensively  determined  be- 
cause of  economic  reasons,  and  has  become  a  very  familiar  characteristic 

alt  should  be  noted  that  this  ratio  method  is  not  a  good  way  of  measuring  the 
potential  dairy  capacity  of  the  sire  (cf.  Yapp42*). 

bHigh  yield  is  essential  to  efficiency  of  production  (cf.  Fig.  29  of  Gaines16*). 


1928}  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  433 

of  breeds  and  individuals.  Fat  percentage  is  a  universally  used  measure 
of  the  chemical  quality  of  milk. 

Many  investigators  seem  to  regard  the  fat  yield  of  a  cow  as  being 
due  to  the  milk  yield  and  fat  percentage.  Thus  Winters40*  cites  the  rec- 
ords of  two  purebred  full  sisters: 

M  F  f  F.C.M. 

No.  1 8,735.2  401.55  4.60  9,517 

No.  2 8,345.5  479.30  5.73  10,528 

and  says  of  them:  "Sister  number  1  has  a  greater  production  of  milk, 
but  number  2  has  a  greater  production  of  fat,  due  to  the  greater  percent 
of  fat  in  her  milk.  This  is  a  case  of  physiological  variation  where  the 
quantitative  variation  favored  one  sister  but  the  qualitative  favored  the 
other  one. "  The  quoted  statement  seems  to  involve  the  same  sort  of 
conception  as  is  involved  in  the  idea  of  securing  a  high-milk  and  high- 
fat-percentage  cow  by  the  crossbreeding  methods  mentioned  in  the  pre- 
vious section.  The  italics  are  the  present  writer's. 

From  a  biological  standpoint  it  is  not  proper  to  regard  fat  yield, 
at  a  given  milk  yield,  as  "due  to"  fat  percentage.  Fat  yield  is  the  direct 
result  of  the  rate  of  fat  secretion  by  the  milk  secreting  cells  and  the 
time  over  which  secretion  continues.  Likewise,  milk  yield  is  the  result 
of  the  rate  of  milk  secretion.  In  one  case  we  are  considering  a  parti- 
cular part  of  the  activity  of  the  mammary  gland,  namely,  its  elabora- 
tion of  milk  fat;  in  the  other  case  we  are  considering  the  entire  mass  of 
the  secretory  product.  Obviously  fat  percentage  is  merely  a  mathemat- 
ical expression  of  the  ratio  (X  100)  of  the  average  rate  of  fat  secretion 
to  the  average  rate  of  milk  secretion.  At  a  given  rate  of  milk  yield  fat 
percentage  is  due  to  the  rate  of  fat  yield ;  certainly  the  rate  of  fat  yield 
is  not,  in  any  biological  sense,  due  to  the  fat  percentage.  The  criticism 
is  offered,  not  so  much  for  the  special  case  quoted,  as  for  its  bearing  on 
the  general  point  of  view. 

While  the  determination  of  fat  percentage  has  been  stimulated  pri- 
marily by  economic  forces,  it  so  happens,  fortunately,  that  it  is  a  very 
good  biological  measure  of  the  properties  of  the  entire  and  normal  milk 
of  the  cow.  There  is  a  high  correlation  between  fat  percentage  and  both 
protein  and  water  percentage,  14*(r  =  .812  and  .916,  respectively)  while, 
roughly,  the  percentage  of  lactose  and  ash  may  be  regarded  as  constant. 
We  have  noted  from  Overman  and  Sanmann's33-  34*  work  that  fat 
percentage  is  very  highly  correlated  with  energy  value  per  unit  of 
milk  (r  =  .9814).  From  the  milk  yield  and  fat  percentage  we  have 
warrant,  therefore,  to  estimate  energy  yield. 

The  energy  yield  affords  an  inclusive,  and  fundamentally  well- 
grounded  measure  of  the  amount  of  work  performed  by  the  cow  in 


434  •       BULLETIN  No.  308  [May, 

milk  secretion.  The  fat  percentage  gives  a  reliable  index  of  the  di- 
rection in  which  the  work  is  performed,  that  is,  the  relative  extent  to 
which  it  is  directed  toward  the  elaboration  of  fat,  of  protein,  and 
of  lactose,  as  shown  in  Fig.  3.  Energy  yield  may  be  regarded  as  the 
primary  variable  in  dairy  production,  expressing  the  quantity  of 
production.  Fat  percentage  may  be  regarded  as  a  secondary  variable, 
expressing  the  kind  of  production. 

SUMMARY  AND  CONCLUSIONS 

The  performance  of  the  dairy  cow  at  the  pail  is  commonly  measured 
by  one  or  both  of  two  expressions — milk  yield  and  fat  yield.  In  Bul- 
letin 245  of  this  Station  (1923)  it  was  suggested  that  the  energy  yield, 
that  is,  the  gross  energy  value  of  the  milk,  is  a  better  measure  of  yield 
than  either  the  milk  or  the  fat.  This  paper  is  intended  to  bring  the 
evidence  on  the  subject  up  to  date.  It  is  based  largely  on  prior  perti- 
nent literature. 

Energy  yield  may  be  estimated  with  a  reasonable  degree  of  accu- 
racy from  the  milk  yield  and  fat  percentage.  The  correlation  between 
fat  percentage  and  energy  value  per  unit  of  milk  is  of  the  order,  r  =  .98 
to  .99.  The  formula  used  in  Bulletin  245  was  F.C.M.  =  AM  +  15F, 
where  F.C.M.  ("fat-corrected  milk")  is  gross  energy  value  in  terms  of 
normal  average  cows'  milk  of  4-percent  fat  content,  M  is  actual  milk 
and  F  is  fat,  all  in  the  same  unit  of  weight.  Evidence  since  accumula- 
ted quite  fully  substantiates  the  accuracy  of  this  formula,  but  indicates 
that  the  energy  value  of  1  pound  of  4-percent  milk  is  about  340  large 
calories  (instead  of  330.6,  as  previously  given).  The  corresponding  cal- 
orie formula  becomes  E  =  51M  (2  %  +/),  where  E  is  energy  in  large 
calories,  M  is  milk  in  pounds,  and  /  is  fat  percentage.  Use  of  the  F.C.M. 
formula  is  continued  because  of  facility  of  computation  and  with  the 
idea  that  the  expression  of  energy  yield  in  calories  might  be  reserved 
for  refined  experimental  work,  where  the  energy  value  is  determined  by 
direct  calorimetry.  The  F.C.M.  formula  appears  to  be  sufficiently  ac- 
curate for  ordinary  work. 

The  nutrients  required  for  lactation  (maintenance  excluded)  per 
pound  of  milk  are  directly  proportional  to  the  energy  value  of  the  milk 
as  computed  by  the  above  formula.  The  correlation  between  fat  per- 
centage and  nutrients  for  lactation  per  pound  of  milk  is  r  =  .648.  It 
seems  probable  that  the  total  feed  consumption  is  also  closely  propor- 
tional to  the  energy  value  of  the  milk.  This  relation  means  practically, 
in  terms  of  money,  that  the  cost  of  milk  production  is  proportional 
to  the  energy  value  of  the  milk.  In  nutritional  work  the  energy  value 


1928}  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  435 

of  the  milk  affords  a  comprehensive  and  well-grounded  expression  of 
yield. 

It  was  previously  concluded  that  in  so  far  as  milk  yield  is  affected 
by  the  composition  of  the  milk,  the  yield  is  inversely  proportional  to 
the  energy  value  per  unit  of  milk,  that  is,  the  energy  yield  is  not  affect- 
ed by  the  fat  percentage  of  the  milk.  This  conclusion  is  here  supported 
by  additional  evidence  from  the  records  of  the  Milking  Shorthorn  and 
Red  Danish  breeds.  The  correlation  between  fat  percentage  and  milk 
yield  is  of  the  order,  r  =  —  .2  to  —  .4;  but  between  fat  percentage  and 
energy  yield,  r  =  0.  As  between  different  cows  a  certain  amount  of 
variability  in  milk  yield  is  due  to  differences  hi  the  composition  of  the 
milk.  This  source  of  variability  is  eliminated  when  the  yield  is  measured 
on  the  energy  basis.  Energy  yields  are  directly  comparable  so  far  as  fat 
percentage  of  the  milk  is  concerned. 

The  lactation  curve  (rate  of  yield  with  time  after  calving)  is  more 
regular  when  expressed  in  terms  of  energy  than  in  terms  of  milk  or  fat. 
Utilizing  the  mechanical  equivalent  of  heat  (1  calorie  =  3084  foot-pounds) 
the  energy  lactation  curve  may  be  translated  directly  in  terms  of  power: 
1  pound  F.C.M.  per  day  =  .022  horsepower.  Measuring  milk  yield  on 
an  energy  basis  puts  the  performance  of  the  cow  on  a  dynamical  basis. 

Considering  milk  yield  on  an  energy  basis  exposes  the  fallacy  of 
attempting  to  breed  increased  dairy  capacity  by  hybridizing  a  high- 
milk,  low-fat-percentage  race  with  a  low-milk,  high-fat-percentage 
race,  in  the  expectation  of  obtaining  a  high-milk,  high-fat-percentage, 
F2  segregate.  The  results  of  several  crossbreeding  experiments  do  not 
promise  improvement  in  energy  yield  capacity,  and  this  may  be  taken 
as  experimental  evidence  that  energy  yield  is  a  more  fundamental  meas- 
ure of  performance  than  is  milk  yield. 

The  biological  significance  of  fat  percentage  is  as  a  measure  of  the 
relative  rates  of  secretion  of  the  fat  as  a  part  and  of  the  milk  as  a  whole. 
At  a  given  milk  yield  the  fat  yield  is  not,  in  any  biological  sense,  due  to 
or  caused  by  the  fat  percentage.  Fat  percentage  is  a  good  index  of  the 
composition  of  the  milk  and  of  its  energy  value. 

Energy  yield  may  be  regarded  as  the  primary  measure  of  yield, 
showing  the  amount  of  work  done  in  milk  secretion.  This  work  may 
be  done  in  different  directions,  that  is,  to  variable  degrees  in  the  elabo- 
ration of  fat,  protein  and  lactose.  Fat  percentage  may  be  regarded 
as  a  secondary  measure  of  yield,  showing  the  direction  in  which  the 
work  is  done. 

From  a  biological  point  of  view  the  essential  measures  of  perform- 
ance of  the  cow  at  the  pail  are  the  energy  yield  and  fat  percentage. 


436  BULLETIN  No.  308  [May, 

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1928]  ENERGY  BASIS  OF  MEASURING  MILK  YIELD  IN  DAIRY  Cows  437 

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"The  last  two  references  were  added  to  the  list  just  before  the  manuscript  was  printed,  and 
therefore  are  not  in  alphabetical  order. 


UNIVERSITY  OF  ILLINOIS-URBANA 


